Applying Fubini's theorem and [1]} yield
\(\int _K f\ast g(t) \eta _x(\tilde{t})dm(t)&=\int _K \left(\int _K f(y)T_{\tilde{y}}g(t)dm(y)\right)\eta _x(\tilde{t})dm(t)\\ &=\int _K \left( \int _K g(t)T_{y}\eta _x(\tilde{t})dm(t)\right)f(y)dm(y)\\ &=\int _K\left(\int _K f(y)T_{y}\eta _x(\tilde{t})dm(y)\right)g(t)dm(t)\) 
